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十角星
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十角星,又稱十芒星,是指一種有十隻尖角,並以十條直線畫成的星星圖形。
幾何學
Quick Facts 正十角星, 對偶 ...
正十角星 | |
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![]() 正十角星形 | |
對偶 | 自身對偶 |
邊 | 10 |
頂點 | 10 |
施萊夫利符號 | 10/3 5/3 |
考克斯特符號(英語:Coxeter–Dynkin diagram) | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
鮑爾斯縮寫 (verse-and-dimensions的wikia:Bowers acronym) | deg![]() |
對稱群 | 二面體群 (D10) |
內角(度) | 72 |
特性 | 星形、外接圓、等邊、等角、isotoxal |
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在幾何學中,十角星是邊自我相交的十邊形。
正十角星只有一種,其施萊夫利符號為{10/3},與所述第二數字差別在繪製十角星時頂點間隔數。[1]
正十角星每邊為,正十角星各邊的長度比例,以及在每個邊的交叉點比例在以下圖形所示。
在幾何學上,只要擁有10個邊、10個角,並可用10邊形容納的圖形即可稱為十角星,其符號以{10/n}表示。只有{10/3}的十角星為正十角星,但還有三種十角星也可被解釋為正十角星。
More information 形式, 多邊形 ...
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與五角星及五邊形相關性
十角星與五角星及五邊形有一定的關連性,當五角星或五邊形截斷邊角時,也可創造出十角星。[4][5][6]
以下列表列出十角星與五角星及五邊形的關連性。
More information 擬正多面體, 等角多邊形 ...
擬正多面體 | 等角多邊形 | 擬正多面體 雙層覆蓋形式 | |
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![]() t{5} = {10} |
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![]() t{5/4} = {10/4} = 2{5/2} |
![]() t{5/3} = {10/3} |
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![]() t{5/2} = {10/2} = 2{5} |
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應用
十角星常出現在伊斯蘭教使用的綺理花磚(英語:Girih tiles)上。[7]
參見
參考文獻
- Barnes, John, Gems of Geometry, Springer: 28–29, 2012 [2015-08-16], ISBN 9783642309649, (原始內容存檔於2019-06-08).
- Regular polytopes, p 93-95, regular star polygons, regular star compounds
- Coxeter, Introduction to Geometry, second edition, 2.8 Star polygons p.36-38
- The Lighter Side of Mathematics: Proceedings of the Eugène Strens Memorial Conference on Recreational Mathematics and its History, (1994), Metamorphoses of polygons, Grünbaum, B.(英語:Branko Grünbaum).
- *Coxeter, Harold Scott MacDonald; Longuet-Higgins, M. S.; Miller, J. C. P. Uniform polyhedra. Philosophical Transactions of the Royal Society of London. Series A. Mathematical and Physical Sciences (The Royal Society). 1954, 246 (916): 411. ISSN 0080-4614. JSTOR 91532. MR 0062446. doi:10.1098/rsta.1954.0003.
- Coxeter, The Densities of the Regular polytopes I, p.43 If d is odd, the truncation of the polygon {p/q} is naturally {2n/d}. But if not, it consists of two coincident {n/(d/2)}'s; two, because each side arises from an original side and once from an original vertex. Thus the density of a polygon is unaltered by truncation.
- Sarhangi, Reza, Polyhedral Modularity in a Special Class of Decagram Based Interlocking Star Polygons, Bridges 2012: Mathematics, Music, Art, Architecture, Culture (PDF): 165–174, 2012 [2015-08-16], (原始內容 (PDF)存檔於2015-02-05).